Level‐cut inhomogeneous filtered Poisson field for two‐phase microstructures

Level‐cut homogeneous filtered Poisson fields developed in (J. Appl. Phys. 2003; 94 (6):3762–3770) to model two‐phase microstructures are defined, and their properties are briefly reviewed. Filtered Poisson fields are sums of randomly scaled and oriented kernels that are centered at the points of homogeneous Poisson fields. The cuts of these fields above specified thresholds are called level‐cut homogeneous filtered Poisson fields. It is shown that an arbitrary inhomogeneous Poisson field becomes homogeneous if observed in new coordinates, and that the mapping relating inhomogeneous and homogeneous Poisson fields can be constructed in a simple manner. This mapping and the model in (J. Appl. Phys. 2003; 94 (6): 3762–3770) provide an efficient algorithm for generating arbitrary inhomogeneous two‐phase microstructures. Developments in (Int. J. Numer. Meth. Engng 2008; DOI: 10.1002/nme.2340 ), using arguments essentially identical to those in (J. Appl. Phys. 2003; 94 (6):3762–3770) to define and generate inhomogeneous Poisson fields, overlook the natural extension of results in (J. Appl. Phys. 2003; 94 (6): 3762–3770) to these fields provided by the mapping constructed in this paper. Copyright © 2008 John Wiley & Sons, Ltd.